ON a Wednesday afternoon in July, sweet-faced, 40-year-old Katherina Richter got into her car outside her Poughkeepsie gift shop and seemingly vanished into the mid-summer air.

Now, six weeks later, police investigating her disappearance are focusing on Manhattan, led here by their only clue Richter’s car, which they recently discovered has been parked unclaimed in a West 87th Street garage since the afternoon she vanished.

Is Katherina Richter living a double life in or near New York City for some reason that cops and her distraught family and boyfriend can’t begin to guess at?

Those who love her say they desperately hope so because police have told them that if she hasn’t run away willfully, the odds are she’s fallen in harm’s way, possibly fatally.

“If she’s living a second life, all right. I’m ready to accept that,” her live-in boyfriend of 15 years, Michael Butigieg, said recently, sobbing almost uncontrollably.

“I just want to know that she’s OK,” he cried. ‘I need to know that she’s OK.”

Richter and Butigieg are Manhattan natives. But 15 years ago, they moved into a fixer-upper Victorian mansion in Poughkeepsie, an hour and a half drive north, to pursue their dream of living and working together as artisans.

Butigieg crafts handmade picture frames. Richter would paint them with whimsical flowers and dragonflies and sell them in the upscale Poughkeepsie gift shop where she’s managing partner.

Lately, the gift shop, Wemyss Inc., in the Galleria Mall, had fallen on hard financial times “but nothing that points to her stealing from the store, ” said Poughkeepsie Det. Sgt. Dave Lundgren.

“There are no piles of money missing,” he said. “You could make a case that she just split out of shame, said Det. Roger Kroll, who wonders if Richter felt she’d let down the good friend from Florida who financed the store.

But cops and Richter’s family see serious problems with the just split scenario.

Richter’s credit cards, bank accounts and passport have been untouched since she hurriedly left the store at 3 p.m. on July 20, telling a co-worker she’d return after running some errands.

If she ran away, what has she been living on?

Richter was the model of stability, her loved ones say.

“No drugs, no drinking, no smoking ” I don’t think she had any vices at all,” said Kroll, who has been investigating Richter’s disappearance since July 21 and told The Post, “I’m glad you called me. I’m at my wit’s end over this one . . . it’s completely out of character for her to disappear.”

Richter has no known friends in the city, and seemingly took nothing with her when she left.

Still, there is the car a blue, four-door, 1985 Volkswagen Golf with no traces of blood or trauma inside or out.

It’s registered to Butigieg, who has passed a polygraph test and is not considered a suspect, according to police.

The car was discovered when the garage owners sent Butigieg a letter saying it would be auctioned off if he didn’t pay the $1,000 parking tab that had built up since 4:30 p.m. June 20, the day Richter disappeared.

The timing means whoever drove the car headed straight for Manhattan, with no stops, to get to the garage in an hour and a half.

When Poughkeepsie cops rushed here to search the car for clues, garage employees ” who couldn’t remember who had dropped it off showed them the single key left by the driver.

It was always Richter’s habit, when she parked in a garage, to remove the car key and pocket the rest of her key chain.

Would a carjacker have bothered to do the same thing?

The cops and Richter’s family think not, and hope that the single key means Richter parked the car herself and then walked away in perfect health, vanishing without a trace into the Upper West Side.

“Our gut hope is she’s still out there and everything’s all right,” said her brother, Alfred, a 38-year-old art dealer who, like the rest of her immediate family, lives near Allentown, Pa.

“Kathy,” he said, his voice breaking. “We love you very much. And we want you back home.”